In a triangle ABC, AC=BC and angle ACB=40. The vertices A,B and C lie on the circumference of a circle. D is a point outside this circle such that DC is perpendicular to BC, BC=DC and the points B...

In a triangle ABC, AC=BC and angle ACB=40. The vertices A,B and C lie on the circumference of a circle. D is a point outside this circle such that DC is perpendicular to BC, BC=DC and the points B and D are on the same side of the line AC. DA cuts the circumference of the circle at E. Find the size of angle DCE.

We are given `bar(AC) cong bar(BC)` with `Delta ABC` inscribed in a circle. `bar(DC)` is drawn on the same side of `bar(AC)` as B such that `bar(DC) _|_ bar(BC)`and `bar(DC) cong bar(BC)` . Then `bar(DA)` intersects the circle at E; we are to find the measure of `/_DCE` :